JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (11): 52-62.doi: 10.6040/j.issn.1671-9352.0.2018.530

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Dynamic analysis of Bertrand game model about taxation of government and subsidy

CAO Hui-rong 1, ZHOU Wei1*, CHU Tong2, ZHOU Jie1   

  1. 1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
    2. School of Law, Zhejiang University of Finance and Economics, Hangzhou 310018, Zhejiang, China
  • Published:2019-11-06

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Abstract: In the context of government implements both subsidy and taxation policies, a dynamics Bertrand game model is established based on bounded rationality. The local asymptotic stability of equilibrium points of the system is analyzed using Jury conditions, the evolution process of the system after equilibrium point instability is discussed by numerical simulation method. It is found that enterprise profit is optimal in Nash equilibrium. The high speed of price adjustment or the low share of government subsidies make the system chaotic, and the profits of enterprises will increase negatively. In order to ensure that enterprises are in the profit mode, the state feedback and parameter adjustment control strategy are adopted to keep the system in Nash equilibrium for a long time. In addition, by analyzing the internal structure of the attraction basin, it is found that the high adjustment speed makes the system bifurcate globally, and the choice of initial decision-making appears unpredictable.

Key words: Bertrand game model, taxation and subsidy, bifurcation, chaos control

CLC Number: 

  • O193
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